Advanced Lane Finding Project¶
The Project¶
The goals/steps of this project are the following:
- Compute the camera calibration matrix and distortion coefficients given a set of chessboard images.
- Apply a distortion correction to raw images.
- Use color transforms, gradients, etc., to create a threshold binary image.
- Apply a perspective transform to rectify binary image ("bird-eye-view").
- Detect lane pixels and fit to the lane boundary.
- Determine the curvature of the lane and vehicle position with respect to center.
- Warp the detected lane boundaries back onto the original image.
- Output visual display of the lane boundaries and numerical estimation of lane curvature and vehicle position
1. Compute the camera calibration matrix and distortion coefficients given a set of chessboard images¶
In [1]:
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.image as mpimg
import glob
import pickle
import cv2
%matplotlib inline
In [2]:
# Read in and make a list of calibration images
# Show all the images for caliration
images = glob.glob('./camera_cal/calibration*.jpg')
ncols = 5
nrows = int(len(images)/ncols)
plt.figure(figsize=(12, 8))
idx = 1
for fname in sorted(images):
img = cv2.imread(fname)
plt.subplot(nrows, ncols, idx)
plt.axis('off')
plt.title(fname.split('/')[-1])
plt.imshow(img)
idx += 1
In [3]:
# Array to store
objpoints = [] # 3D points in real world space
imgpoints = [] # 2D points in image plane
# Prepare object points, like (0, 0, 0), (1,0,0), (),...(8,5,0)
objp = np.zeros((9*6,3), np.float32)
objp[:,:2] = np.mgrid[0:9, 0:6].T.reshape(-1,2) # x, y coordinates
images = glob.glob('./camera_cal/calibration*.jpg')
for fname in images:
# read in each image
img = cv2.imread(fname)
img_size = (img.shape[1], img.shape[0])
# convert image to grayscale
gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
# find the chessboard corners
ret, corners = cv2.findChessboardCorners(gray,(9,6), None)
# if corners are found, add objects points, image points
if ret == True:
imgpoints.append(corners)
objpoints.append(objp)
# draw and display the corners
img = cv2.drawChessboardCorners(img,(9,6), corners, ret)
plt.figure()
plt.imshow(img)
# Camera calibration, given object points, image points, and the shape of the grayscale image
ret, mtx, dist, rvecs, tvecs = cv2.calibrateCamera(objpoints, imgpoints, gray.shape[::-1], None, None)
# ret, mtx, dist, rvecs, tvecs = cv2.calibrateCamera(objpoints, imgpoints, img_size, None, None)
2. Apply a distortion correction to raw images.¶
In [4]:
def undistort_image(img):
# Undistort a test image
img = cv2.undistort(img, mtx, dist, None, mtx)
return img
# Show a result
image_file = './camera_cal/calibration2.jpg'
img = cv2.imread(image_file)
img = img[...,::-1] # RGB -> BGR
undistorted = undistort_image(img)
f, (ax1, ax2) = plt.subplots(1, 2, figsize=(24, 9))
f.tight_layout()
ax1.set_title('Original Image', fontsize=50)
ax1.imshow(img)
ax2.set_title('Undistorted Image', fontsize=50)
ax2.imshow(undistorted)
plt.subplots_adjust(left=0., right=1, top=0.9, bottom=0.)
In [5]:
# Apply undistort_image() function to images in camera_cal and test_images folders
# and save the results to output_images folder
for idx, fname in enumerate(images):
img = cv2.imread(fname)
img = cv2.cvtColor(img, cv2.COLOR_BGR2RGB)
# apply undistort image
dst = undistort_image(img)
# save the results
bgr_img = cv2.cvtColor(dst, cv2.COLOR_RGB2BGR)
cv2.imwrite("./output_images/camera_cal_output/" + "undistorted_cal" + str(idx+1) + ".jpg", bgr_img)
image_test = glob.glob('./test_images/test*.jpg')
for idx, fname in enumerate(image_test):
img = cv2.imread(fname)
img = cv2.cvtColor(img, cv2.COLOR_BGR2RGB)
# apply undistort image
dst = undistort_image(img)
# save the results
bgr_img = cv2.cvtColor(dst, cv2.COLOR_RGB2BGR)
cv2.imwrite("./output_images/test_images_output/" + "undistorted_test" + str(idx+1) + ".jpg", bgr_img)
In [6]:
# Visualizing the undistorted images in camera_cal
results = glob.glob('./output_images/camera_cal_output/*.jpg')
ncols = 5
nrows = int(len(results)/ncols)
plt.figure(figsize=(12, 8))
idx = 1
for fname in sorted(results):
rs = cv2.imread(fname)
plt.subplot(nrows, ncols, idx)
plt.axis('off')
plt.title(fname.split('/')[-1])
plt.imshow(rs)
idx += 1
3. Use color transforms, gradients, etc., to create a threshold binary image.¶
In [7]:
from utils.thresholds import *
# Plot the result
print("Thresholded Binary")
f, (ax1, ax2) = plt.subplots(1, 2, figsize=(16,8))
f.tight_layout()
img3= cv2.imread('./output_images/test_images_output/undistorted_test1.jpg')
binary = toBinary(img3)
ax1.imshow(img3)
ax1.set_title('Undistorted Image', fontsize=40)
ax2.imshow(binary, cmap='gray')
ax2.set_title('Thresholded Binary Image', fontsize=40)
plt.subplots_adjust(left=0, right=1, top=0.9, bottom=0)
4. Apply a perspective transform to rectify binary image ("bird-eye-view")¶
In [8]:
def warper(image):
# offset for dst points
offset = 350
# Source points
src = np.float32([[[ 610, 450]],
[[ 680, 450]],
[[ img_size[0]-300, 680]],
[[ 380, 680]]])
# Result points
dst = np.float32([[offset, 0],
[img_size[0]-offset, 0],
[img_size[0]-offset, img_size[1]],
[offset, img_size[1]]])
# Given src and dst points, calculate the perspective transform matrix
M = cv2.getPerspectiveTransform(src, dst)
# Warp the image using OpenCV warpPerspective()
warped = cv2.warpPerspective(image, M, img_size)
# Return the resulting image and matrix
return warped, M
warped, perspective_M = warper(binary)
print('Top down image')
f, (ax1, ax2) = plt.subplots(1, 2, figsize=(16,8))
f.tight_layout()
ax1.set_title("Binary Image", fontsize=30)
ax1.imshow(binary, cmap='gray')
ax2.set_title("Top down Image", fontsize=30)
ax2.imshow(warped, cmap='gray')
Out[8]:
In [9]:
# Take a histogram of the bottom half of the image
histogram = np.sum(warped[int(warped.shape[0]/2):,:], axis=0)
plt.plot(histogram);
5. Detect lane pixels and fit to the lane boundary¶
In [10]:
# Read in a thresholded image
# warped = mpimg.imread(warped)
# Window settings
window_width = 50
window_height = 80 # Break image into 9 vertical layers since image height is 720
margin = 100 # How much to slide left and right for searching
def window_mask(width, height, img_ref, center, level):
output = np.zeros_like(img_ref)
output[int(img_ref.shape[0]-(level+1)*height):int(img_ref.shape[0]-level*height),max(0,int(center-width/2)):min(int(center+width/2),img_ref.shape[1])] = 1
return output
def find_window_centroids(image, window_width, window_height, margin):
window_centroids = [] # Store the (left,right) window centroid positions per level
leftx = []
rightx = []
window = np.ones(window_width) # Create our window template that we will use for convolutions
# First find the two starting positions for the left and right lane by using np.sum to get the vertical image slice
# and then np.convolve the vertical image slice with the window template
# Sum quarter bottom of image to get slice, could use a different ratio
l_sum = np.sum(image[int(3*image.shape[0]/4):,:int(image.shape[1]/2)], axis=0)
l_center = np.argmax(np.convolve(window,l_sum))-window_width/2
r_sum = np.sum(image[int(3*image.shape[0]/4):,int(image.shape[1]/2):], axis=0)
r_center = np.argmax(np.convolve(window,r_sum))-window_width/2+int(image.shape[1]/2)
# Add what we found for the first layer
window_centroids.append((l_center,r_center))
leftx.append(l_center)
rightx.append(r_center)
# Go through each layer looking for max pixel locations
for level in range(1,(int)(image.shape[0]/window_height)):
# convolve the window into the vertical slice of the image
image_layer = np.sum(image[int(image.shape[0]-(level+1)*window_height):int(image.shape[0]-level*window_height),:], axis=0)
conv_signal = np.convolve(window, image_layer)
# Find the best left centroid by using past left center as a reference
# Use window_width/2 as offset because convolution signal reference is at right side of window, not center of window
offset = window_width/2
l_min_index = int(max(l_center+offset-margin,0))
l_max_index = int(min(l_center+offset+margin,image.shape[1]))
prev_l_center = l_center
l_center = np.argmax(conv_signal[l_min_index:l_max_index])+l_min_index-offset
# Find the best right centroid by using past right center as a reference
r_min_index = int(max(r_center+offset-margin,0))
r_max_index = int(min(r_center+offset+margin,image.shape[1]))
prev_r_center = r_center
r_center = np.argmax(conv_signal[r_min_index:r_max_index])+r_min_index-offset
# Add what we found for that layer
window_centroids.append((l_center,r_center))
leftx.append(l_center)
rightx.append(r_center)
return window_centroids, leftx, rightx
window_centroids, leftx, rightx = find_window_centroids(warped, window_width, window_height, margin)
# If we found any window centers
if len(window_centroids) > 0:
# Points used to draw all the left and right windows
l_points = np.zeros_like(warped)
r_points = np.zeros_like(warped)
# Go through each level and draw the windows
for level in range(0,len(window_centroids)):
# Window_mask is a function to draw window areas
l_mask = window_mask(window_width,window_height,warped,window_centroids[level][0],level)
r_mask = window_mask(window_width,window_height,warped,window_centroids[level][1],level)
# Add graphic points from window mask here to total pixels found
l_points[(l_points == 255) | ((l_mask == 1) ) ] = 255
r_points[(r_points == 255) | ((r_mask == 1) ) ] = 255
# Draw the results
template = np.array(r_points+l_points,np.uint8) # add both left and right window pixels together
zero_channel = np.zeros_like(template) # create a zero color channel
template = np.array(cv2.merge((zero_channel,template,zero_channel)),np.uint8) # make window pixels green
out_img = np.dstack((warped, warped, warped))*255
warpage = np.array(out_img,np.uint8) # making the original road pixels 3 color channels
output = cv2.addWeighted(warpage, 1, template, 0.5, 0.0) # overlay the orignal road image with window results
# If no window centers found, just display orginal road image
else:
output = np.array(cv2.merge((warped,warped,warped)),np.uint8)
# Display the final results
print('Left and right points')
print ('Left: ',leftx)
print ('Right: ',rightx)
print('')
print('Fitted image')
f, (ax1, ax2) = plt.subplots(1, 2, figsize=(16,8))
f.tight_layout()
ax1.set_title("Warped Image", fontsize=30)
ax1.imshow(warped, cmap='gray')
ax2.set_title("Fitted image", fontsize=30)
ax2.imshow(output)
Out[10]:
6. Determine the curvature of the lane and vehicle position with respect to center¶
In [11]:
# to cover same y-range as image
ploty = np.linspace(0, 719, num=9)
def curvature(leftx, rightx):
leftx = np.asarray(leftx[::-1]) # Reverse to match top-to-bottom in y
rightx = np.asarray(rightx[::-1]) # Reverse to match top-to-bottom in y
# Fit a second order polynomial to pixel positions in each fake lane line
left_fit = np.polyfit(ploty, leftx, 2)
left_fitx = left_fit[0]*ploty**2 + left_fit[1]*ploty + left_fit[2]
leftx_int = left_fit[0]*720**2 + left_fit[1]*720 + left_fit[2]
right_fit = np.polyfit(ploty, rightx, 2)
right_fitx = right_fit[0]*ploty**2 + right_fit[1]*ploty + right_fit[2]
rightx_int = right_fit[0]*720**2 + right_fit[1]*720 + right_fit[2]
position = ((rightx_int+leftx_int)/2)-50
center = abs(640 - ((rightx_int+leftx_int)/2))
y_eval = np.max(ploty)
# Define conversions in x and y from pixels space to meters
ym_per_pix = 30/720 # meters per pixel in y dimension
xm_per_pix = 3.7/700 # meters per pixel in x dimension
# Fit new polynomials to x,y in world space
left_fit_cr = np.polyfit(ploty*ym_per_pix, leftx*xm_per_pix, 2)
right_fit_cr = np.polyfit(ploty*ym_per_pix, rightx*xm_per_pix, 2)
# Calculate the new radii of curvature
left_curverad = ((1 + (2*left_fit_cr[0]*y_eval*ym_per_pix + left_fit_cr[1])**2)**1.5) / np.absolute(2*left_fit_cr[0])
right_curverad = ((1 + (2*right_fit_cr[0]*y_eval*ym_per_pix + right_fit_cr[1])**2)**1.5) / np.absolute(2*right_fit_cr[0])
return position, center, leftx, rightx, left_fitx, right_fitx, left_curverad, right_curverad
position, center, leftx, rightx, left_fitx, right_fitx, left_curverad, right_curverad = curvature(leftx, rightx)
# Plot up the data
mark_size = 3
plt.plot(leftx, ploty, 'o', color='red', markersize=mark_size)
plt.plot(rightx, ploty, 'o', color='blue', markersize=mark_size)
plt.xlim(0, 1280)
plt.ylim(0, 720)
plt.plot(left_fitx, ploty, color='green', linewidth=3)
plt.plot(right_fitx, ploty, color='green', linewidth=3)
plt.gca().invert_yaxis() # to visualize as we do the images
# Now our radius of curvature is in meters
print('Left:',left_curverad, 'm - Right:', right_curverad, 'm')
7. Warp the detected lane boundaries back onto the original image.¶
In [12]:
def warpBack(image, warp, persp_M, le_fitx, ri_fitx):
Minv = np.linalg.inv(persp_M)
# Create an image to draw the lines on
warp_zero = np.zeros_like(warp).astype(np.uint8)
color_warp = np.dstack((warp_zero, warp_zero, warp_zero))
# Recast the x and y points into usable format for cv2.fillPoly()
pts_left = np.array([np.transpose(np.vstack([le_fitx, ploty]))])
pts_right = np.array([np.flipud(np.transpose(np.vstack([ri_fitx, ploty])))])
pts = np.hstack((pts_left, pts_right))
# Draw the lane onto the warped blank image
cv2.fillPoly(color_warp, np.int_([pts]), (0,255,0))
# Warp the blank back to original image space using inverse perspective matrix (Minv)
newwarp = cv2.warpPerspective(color_warp, Minv, (image.shape[1], image.shape[0]))
# Combine the result with the original image
result = cv2.addWeighted(image, 1, newwarp, 0.3, 0)
return result
plt.imshow(warpBack(img3, warped, perspective_M, left_fitx, right_fitx))
Out[12]:
8. Output visual display of the lane boundaries and numerical estimation of lane curvature and vehicle position¶
In [13]:
f, (ax1, ax2) = plt.subplots(1, 2, figsize=(16,8))
f.tight_layout()
ax1.set_title("Original Image", fontsize=30)
ax1.imshow(img3)
ax2.set_title("Curvature and vehicle position", fontsize=30)
if position == 640:
ax2.text(50, 100, 'Vehicle is in the center', style='italic', color='white', fontsize=16)
elif position < 640:
ax2.text(50, 100, 'Vehicle is {:.2f}m left of center'.format(center*3.7/700),
style='italic', color='white', fontsize=16)
else:
ax2.text(50, 100, 'Vehicle is {:.2f}m right of center'.format(center*3.7/700),
style='italic', color='white', fontsize=16)
ax2.text(50, 150, 'Radius of curvature is {}m'.format(int((left_curverad + right_curverad)/2)),
style='italic', color='white', fontsize=16)
ax2.imshow(warpBack(img3, warped, perspective_M, left_fitx, right_fitx))
Out[13]:
9. The Final Pipeline¶
In [14]:
class Line():
def __init__(self):
# was the line detected in the last iteration?
self.detected = False
# x values of the last n fits of the line
self.recent_xfitted = []
#average x values of the fitted line over the last n iterations
self.bestx = None
#polynomial coefficients averaged over the last n iterations
self.best_fit = None
#polynomial coefficients for the most recent fit
self.current_fit = [np.array([False])]
#radius of curvature of the line in some units
self.radius_of_curvature = None
#distance in meters of vehicle center from the line
self.line_base_pos = None
#difference in fit coefficients between last and new fits
self.diffs = np.array([0,0,0], dtype='float')
#x values for detected line pixels
self.allx = None
#y values for detected line pixels
self.ally = None
def lane_finding(img):
undistorded = undistort_image(img)
final_binary = toBinary(undistorded)
final_warped, final_perspective_M = warper(final_binary)
window_cent, lex, rix = find_window_centroids(final_warped, window_width, window_height, margin)
position, center, leftx, rightx, left_lane.recent_xfitted, right_lane.recent_xfitted, left_lane.radius_of_curvature, right_lane.radius_of_curvature = curvature(lex, rix)
alpha = 0.5
if left_lane.bestx == None:
left_lane.bestx = left_lane.recent_xfitted
else :
left_lane.recent_xfitted = left_lane.recent_xfitted * ( 1 - alpha) + alpha * left_lane.bestx
if right_lane.bestx == None:
right_lane.bestx = right_lane.recent_xfitted
else :
right_lane.recent_xfitted = right_lane.recent_xfitted * ( 1 - alpha) + alpha * right_lane.bestx
#Sanity check
left_lane.detected = False
right_lane.detected = False
max_distance = 0
min_distance = 10000
for i in range(len(left_lane.recent_xfitted)) :
point_distance = right_lane.recent_xfitted[i] - left_lane.recent_xfitted[i]
if point_distance > max_distance:
max_distance = point_distance
if point_distance < min_distance:
min_distance = point_distance
if (min_distance > 710) and (max_distance < 900):
left_lane.detected = True
right_lane.detected = True
if not left_lane.detected:
left_lane.recent_xfitted = left_lane.bestx
else:
left_lane.bestx = left_lane.recent_xfitted
if not right_lane.detected:
right_lane.recent_xfitted = right_lane.bestx
else:
right_lane.bestx = right_lane.recent_xfitted
result = warpBack(img, final_warped, final_perspective_M, left_lane.recent_xfitted, right_lane.recent_xfitted)
# Print the distances from center on video
if (center*3.7/700) < 0.01:
cv2.putText(result, 'Vehicle is in the center', (50,80),
fontFace = 16, fontScale = 1, color=(255,255,255), thickness = 2)
elif center < 640:
cv2.putText(result, 'Vehicle is {:.2f}m left of center'.format(center*3.7/700), (50,80),
fontFace = 16, fontScale = 1, color=(255,255,255), thickness = 2)
else:
cv2.putText(result, 'Vehicle is {:.2f}m right of center'.format(center*3.7/700), (50,80),
fontFace = 16, fontScale = 1, color=(255,255,255), thickness = 2)
# Print the radius of curvature on video
cv2.putText(result, 'Radius of Curvature {}(m)'.format(int((left_lane.radius_of_curvature + right_lane.radius_of_curvature)/2)), (50,140),
fontFace = 16, fontScale = 1, color=(255,255,255), thickness = 2)
return result
# Lane Finding
print('Test Lane Finding Algorithm')
left_lane = Line()
right_lane = Line()
f, (ax1, ax2) = plt.subplots(1, 2, figsize=(16,8))
f.tight_layout()
ax1.set_title("Original Image", fontsize=30)
ax1.imshow(img)
ax2.set_title("Lane Detected", fontsize=30)
ax2.imshow(lane_finding(img))
Out[14]:
10. Test on The Project Video¶
In [15]:
# Import everything needed to edit/save/watch the video clips
from moviepy.editor import VideoFileClip
from IPython.display import HTML
left_lane = Line()
right_lane = Line()
video_output = "project_video_result.mp4"
input_video = VideoFileClip("../CarND-Advanced-Lane-Lines/project_video.mp4")
output = input_video.fl_image(lane_finding)
%time output.write_videofile(video_output, audio = False)
HTML("""
<video width="960" height="540" controls>
<source src="{0}">
</video>
""".format(video_output))
Out[15]: